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The theory of the exponential differential equations of semiabelian varieties

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Abstract

The complete first-order theories of the exponential differential equations of semiabelian varieties are given. It is shown that these theories also arise from an amalgamation-with-predimension construction in the style of Hrushovski. The theories include necessary and sufficient conditions for a system of equations to have a solution. The necessary conditions generalize Ax’s differential fields version of Schanuel’s conjecture to semiabelian varieties. There is a purely algebraic corollary, the “Weak CIT” for semiabelian varieties, which concerns the intersections of algebraic subgroups with algebraic varieties.

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  1. Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford, OX1 3LB, UK

    Jonathan Kirby

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  1. Jonathan Kirby
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Correspondence to Jonathan Kirby.

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This paper was written while the author was at the University of Oxford and the University of Illinois at Chicago. Supported by the EPSRC fellowship EP/D065747/1.

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Kirby, J. The theory of the exponential differential equations of semiabelian varieties. Sel. Math. New Ser. 15, 445 (2009). https://doi.org/10.1007/s00029-009-0001-7

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